Divide 3 – 2x + 2x2 by (2-x) and verify the division algorithm.
Answers
Step-by-step explanation:
degree (-x+2). <br>
quotient = (-2x-3) and remainder = 9 <br>
(quotient
divisor) + remainder <br>
<br>
<br>
<br>
<br> = dividend. <br> Thus, (quotient
divisor)+ remainder = dividend. <br> Hence, the division algorithm is verified.
Step-by-step explanation:
Given :-
3 - 2x + 2x²
To find :-
Divide 3-2x + 2x² by (2-x) and verify the division algorithm.
Solution :-
Given Polynomial is 3-2x+2x²
On writing it in the standard form 2x²-2x+3
2-x can be written as -x+2
On dividing 2x²-2x+3 by (-x+2) then
-x+2 ) 2x²-2x+3 (-2x -2
2x²-4x
(-) (+)
__________
0 +2x +3
2x -4
(-) (+)
___________
7
____________
Quotient = -2x-2
Remainder = 7
Check :-
We know that
Division Algorithm on Polynomials is
p(x) = g(x)×q(x) +r(x)
Now on taking RHS
=> g(x)×q(x) +r(x)
=> (2-x) ×(-2x-2) + 7
=> 2(-2x-2) -x(-2x-2) +7
=> -4x-4 +2x²+2x+7
=> 2x²+(2x-4x)+(7-4)
=> 2x²-2x+3
=> 3-2x+2x²
=> Given Polynomial
Verified the given relations in the given problem
Answer :-
Quotient = -2x-2
Remainder = 7
Used formulae:-
Division Algorithm on Polynomials is
p(x) = g(x)×q(x) +r(x)
Where , p(x) = Dividend
- g(x) = Divisor
- q(x)=quotient
- r(x)=remainder